The BHT study by Harman that has so long been used to sell it (and by extension, other "antioxidants") is "the usual nonsense."
Harman (who has, sadly, recently had life ripped from him by the aging process) took a small groups (10 mice each -- you need ≈50 mice in each group to get a statistically-significant readout of mean and max LS in mice) of abnormally short-lived, sickly LAF mice (mean lifespan: 14.5± 4.6 months), and threw a bunch of different single and/or combination antioxidants and vitamins at them. This is typical of the vast majority of claims of "extended lifespan" from supplement use.A normal, healthy, well-husbanded, non-genetically-fucked-up mouse given no special treatment will on av'g live twice as long as these mice: ~900 days (≈30 months), with a maximum (tenth-decile survivorship) LS of 1100 d, as is routine in the standard control groups in studies run by people who know what they're doing (Spindler, Weindruch, Miller, etc). But in report after report of 'life extension' in mice, NONE of the animals even live THIS long (or at best, the INTERVENTION group does).
Some of the antioxidants and supplements nothing; two synthetic antioxidants (2-MEA and huge doses of BHT) allowed mice to live longer than their miserably short-lived cousins. BHT partially normalized this miserably-short life mean LS (at 0.25% of diet, 17.0± 5.0 mo; at 0.50% of diet, 20.9± 4.7 mo).(1) Note the huge variability, and the short lives in all the animals in the study, whether treated with BHT or not. This is where you get the ridiculous claim of a 45% increase in lifespan from BHT. There was no ostensible effect on maximum LS: it did look on the survival curve as if the max LS might have been increased, but it's impossible to say when you have so few mice -- but (again) even if it ostensibly did, it's not real maximum lifespan, but a partial normalization of a miserably-short life.
Reference
1: Harman D. Free radical theory of aging: effect of free radical reaction inhibitors on the mortality rate of male LAF mice. J Gerontol. 1968 Oct;23(4):476-82. PubMed PMID: 5723482.